{"paper":{"title":"On interrelations between strongly, weakly and chord separated set-systems (a geometric approach)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A.V. Karzanov, G.A. Koshevoy, V.I. Danilov","submitted_at":"2018-05-24T10:41:48Z","abstract_excerpt":"We consider three types of set-systems that have interesting applications in algebraic combinatorics and representation theory: maximal collections of the so-called strongly separated, weakly separated, and chord separated subsets of a set $[n]=\\{1,2,\\ldots,n\\}$. These collections are known to admit nice geometric interpretations; namely, they are bijective, respectively, to rhombus tilings on the zonogon $Z(n,2)$, combined tilings on $Z(n,2)$, and fine zonotopal tilings (or `cubillages') on the 3-dimensional zonotope $Z(n,3)$. We describe interrelations between these three types of set-system"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09595","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}